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8/3/2019 Data Algorithm And Design
1/46
Eo`kr
S/OA/ VZAIZMH OMHK SEIOMP[ZKS
= Pa yzepk mo mliazepbh mo` m vzaizmh pa ehvlkhkopJ{jjlk Sazp
: Pa yzepk mo mliazepbh mo` m vzaizmh pa ehvlkhkop
Leokmz Skmzcb
3 Pa yzepk mo mliazepbh mo` m vzaizmh pa ehvlkhkop
Jeomzu Skmzcb
0 Pa yzepk mo mliazepbh mo` m vzaizmh pa ehvlkhkop
]{ecn Sazp
; Pa yzepk mo mliazepbh mo` m vzaizmh pa ehvlkhkop
jzkm`pb gezsp skmzcb
7 Pa yzepk mo mliazepbh mo` m vzaizmh pa ehvlkhkop
`kvpb gezsp skmzcb
9 Pa yzepk mo mliazepbh mo` m vzaizmh pa ehvlkhkop
Ca{opeoi Sazp
2 Pa yzepk mo mliazepbh mo` m vzaizmh pa ehvlkhkop
hmpzer cbmeo
h{lpevlecmpeao
5 Pa yzepk mo mliazepbh mo` m vzaizmh pa ehvlkhkop
mcpewepu sklkcpeao vzajlkh
=6 Pa yzepk mo mliazepbh mo` m vzaizmh pa ehvlkhkop
laoiksp cahhao s{jsk}{kock
== Pa yzepk mo mliazepbh mo` m vzaizmh pa ehvlkhkop
@ednspzms mlia gaz seoilk sa{zck sbazpksp vmpb/
8/3/2019 Data Algorithm And Design
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Vzaizmh Oa(=
MEH4 Pa yzepk mo mliazepbh mo` m vzaizmh pa ehvlkhkop J{jjlk Sazp/
MLIAZEPBH
"J{jjlk Sazp% J[JJLK "@MPM, O%
Bkzk @MPM es mo mzzmu yepb O klkhkops/ Pbes mliazepbh sazps pbk klkhkops eo @MPM/
=/ Zkvkmp Spkvs : mo` 3 gaz N8= pa O(=/:/
Skp VPZ 48 =/ ^Eoepemletks vmss vaeopkz VPZ/X
3/ Zkvkmp ybelk VPZ
vzeopg"*kopkz pbk o{hjkz ag klkhkops eo pbk mzzmu*%>
8/3/2019 Data Algorithm And Design
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scmog"*+`*,'o%>
vzeopg"*kopkz pbk klkhkops ag pbk mzzmu*%>
gaz"e86>ee..%
~
scmog"*+`*,'m^eX%>
x
gaz"e86>ee..%
~
gaz"d8e.=>dd..%
~
eg"m^eX?m^dX%
~
pkhv8m^eX>
m^eX8m^dX>
m^dX8pkhv>
x
x
x
vzeopg"*pbk sazpk` mzzmu es\o*%>
gaz"e86>ee..%
~
vzeopg"*+`\o*,m^eX%>
x
ikpcb"%>
x
8/3/2019 Data Algorithm And Design
4/46
A[PV[P4
kopkz pbk o{hjkz ag klkhkops eo pbk mzzmu;
kopkz pbk klkhkops ag pbk mzzmu;
0
3
:
=
pbk sazpk` mzzmu es
=
:
3
0
;
8/3/2019 Data Algorithm And Design
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Vzaizmh Oa(:
MEH4 Pa yzepk mo mliazepbh mo` m vzaizmh pa ehvlkhkop Leokmz Skmzcb/
MLIAZEPBH
"Leokmz Skmzcb% LEOKMZ "@MPM, O, EPKH, LAC%
Bkzk @MPM es m iewko mzzmu ag O klkhkops, mo` EPKH es m iewko epkh ag eogazhmpeao/
Pbes mliazepbh geo`s pbk lacmpeao LAC ag EPKH eo @MPM, az skps LAC 486 eg pbk skmzcb
es {os{cckssg{l/
=/ ^Eoskzp EPKH mp pbk ko` ag @MPM/X Skp @MPM^O.=X 48EPKH/:/ ^Eoepemletk ca{opkz/X Skp LAC 48=/3/ ^Skmzcb gaz EPKH/X
Zkvkmp ybelk @MPM^LACX-8 EPKH4
Skp LAC48LAC.=/
^Ko` ag laav/X
0/ ^S{cckssg{l1X Eg LAC 8 O.=, pbko4 Skp LAC 486/;/ Krep/
VZAIZMH PA EHVLKHKOP LEOKMZ SKMZCB
#eocl{`k
vzeopg"*kopkz pbk o{hjkz ag klkhkops eo pbk mzzmu*%>
scmog"*+`*,'o%>
vzeopg"*kopkz pbk klkhkops ag pbk mzzmu*%>
8/3/2019 Data Algorithm And Design
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gaz"e86>ee..%
~
scmog"*+`*,'m^eX%>
x
vzeopg"*kopkz pbk klkhkop ua{ ymop pa skmzcb*%>
scmog"*+`*,'epkh%>
gaz"e86>ee..%
~
eg"m^eX88epkh%
~
c8=>
lac8e>
x
x
eg"c88=%
~
vzeopg"*epkh es mp lacmpeao8+`*,lac.=%>
x
klsk
~
vzeopg"*epkh oap eo pbk lesp*%>
x
ikpcb"%>
x
8/3/2019 Data Algorithm And Design
7/46
A[PV[P4
kopkz pbk o{hjkz ag klkhkops eo pbk mzzmu;
kopkz pbk klkhkops ag pbk mzzmu==3:
=0
=;
:6
kopkz pbk klkhkop ua{ ymop pa skmzcb3:
epkh es mp lacmpeao8:
kopkz pbk o{hjkz ag klkhkops eo pbk mzzmu;
kopkz pbk klkhkops ag pbk mzzmu:=
=
79
;0
30
kopkz pbk klkhkop ua{ ymop pa skmzcb56
epkh oap eo pbk lesp
8/3/2019 Data Algorithm And Design
8/46
Vzaizmh Oa(3
MEH4 Pa yzepk mo mliazepbh mo` m vzaizmh pa ehvlkhkop Jeomzu Skmzcb/
MLIAZEPBH
"Jeomzu Skmzcb% JEOMZU "@MPM, LJ, [J, EPKH, LAC%
Bkzk @MPM es m sazpk` mzzmu yepb laykz ja{o` LJ mo` {vvkz ja{o` [J, mo` EPKH es m
iewko epkh ag eogazhmpeao/ Pbk wmzemjlks JKI, KO@ mo` HE@ `koapk, zksvkcpewklu, pbk
jkieooeoi, ko` mo` he``lk lacmpeaos ag m skihkop ag klkhkops ag @MPM/ Pbes mliazepbh
geo`s pbk lacmpeao ag m skihkop ag klkhkops ag @MPM/ Pbes mliazepbh geo`s pbk lacmpeaoLAC ag EPKH eo @MPM az skps LAC 8 O[LL/
=/ ^Eoepemletk skihkop wmzemjlks/XSkp JKI 48 LJ, KO@ 48[J mo` HE@ 8 EOP""JKI.KO@%!:%/
:/ Zkvkmp Spkvs 3 mo` 0 ybelk JKI
8/3/2019 Data Algorithm And Design
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VZAIZMH PA EHVLKHKOP JEOMZU SKMZCB
#eocl{`k
vzeopg"*kopkz pbk o{hjkz ag klkhkops eo pbk mzzmu*%>
scmog"*+`*,'o%>
vzeopg"*kopkz pbk klkhkops eo pbk mzzmu*%>
gaz"e86>ee..%
~
scmog"*+`*,'m^eX%>
x
vzeopg"*kopkz pbk epkh ua{ ymop pa skmzcb*%>
scmog"*+`*,'epkh%>
beib8o>
he`8""lay.beib%!:%>
ybelk"lay
8/3/2019 Data Algorithm And Design
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eg"m^he`X88epkh%
~
vzeopg"*epkh es vzkskop mp lacmpeao +`*,he`.=%>
x
klsk
~
vzeopg"*epkh oap eo pbk lesp*%>
x
ikpcb"%>
x
A[PV[P4
kopkz pbk o{hjkz ag klkhkops eo pbk mzzmu7
kopkz pbk klkhkops eo pbk mzzmu97
;0
30
:3
=9
;
kopkz pbk epkh ua{ ymop pa skmzcb:3
epkh es vzkskop mp lacmpeao 0
kopkz pbk o{hjkz ag klkhkops eo pbk mzzmu;
kopkz pbk klkhkops eo pbk mzzmu;
0
3:
=
kopkz pbk epkh ua{ ymop pa skmzcb7
epkh oap eo pbk lesp
8/3/2019 Data Algorithm And Design
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Vzaizmh Oa(0
MEH4 Pa yzepk mo mliazepbh mo` m vzaizmh pa ehvlkhkop ]{ecn Sazp/
MLIAZEPBH
][ECNSAZP"M,v,z%
=/ eg v
8/3/2019 Data Algorithm And Design
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n8m^eX>
m^eX8m^dX>
m^dX8n>
x
eop svlep"eop m^X,eop gezsp,eop lmsp%
~
eop zeibp,lkgp,w,pkhv>
w8m^gezspX>
lkgp8lmsp>
zeibp8gezsp.=>
`a
~
ybelk"zeibp
8/3/2019 Data Algorithm And Design
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ybelk"zeibp
symv"m,gezsp,lkgp%>
zkp{zo"lkgp%>
x
wae` }sazp"eop m^X,eop gezsp,eop lmsp%
~
eop s86>
eg"gezsp
clzscz"%>
ggl{sb"sp`eo%>
vzeopg"*\oBay hmou klkhkops ua{ ymop pa sazp*%>
scmog"*+`*,'o%>
vzeopg"*\okopkz pbk wml{ks*%>
gaz"e86>ee..%
scmog"*+`*,'m^eX%>
}sazp"m,6,o(=%>
vzeopg"*\osazpk` lesp es*%>
gaz"e86>ee..%
vzeopg"*\o+`\o*,m^eX%>
ikpcb"%>
x
8/3/2019 Data Algorithm And Design
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A[PV[P4
Bay hmou klkhkops ua{ ymop pa sazp;
kopkz pbk wml{ks:=
=
03
=;
5
sazpk` lesp es
=
5
=;
:=
03
8/3/2019 Data Algorithm And Design
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Vzaizmh Oa(;
MEH4 Pa yzepk mo mliazepbh mo` m vzaizmh pa ehvlkhkop jzkm`pb gezsp
skmzcb/
MLIAZEPBH
JGS"I,s%
=/gaz kmcb wkzpkr { w^IX(~sx
;/ calaz^sXIZMU
7/ `^sX6
9/ ^sXOEL
5/ KO][K[K"],s%
=6/ ybelk ]
==/ `a {@K][K[K"]%
=:/ gaz kmcb w M`d^{X
=3/ `a eg calaz^wX8 YBEPK
=0/
=7/
=9/ KO][K[K"],w%
=2/ calaz^{XJLMCN
VZAIZMH PA EHVKHKOP JZKM@PB GEZSP SKMZCB
8/3/2019 Data Algorithm And Design
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# eocl{`k
x>
Spz{cp wkzpkr
~
eop wesep>
eop wkzpkr Qoa>
cbmz eoga>
eop vmpb(lkoipb>
K`ik $k`ikQvpz>
x>
Sp{cp ]
~
eop eoga>
] $ okrp>
x>
clmss jzkm`pb QgezspQskmzcb
~
v{jlec4wae` pmjlk"eop,eop hmpzer^setkX^setkX,wkzpkr wkzp^setkX%>
K`ik $eoskzpQwkzpkr"eop,k`ik$%>
8/3/2019 Data Algorithm And Design
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wae` jgs "eop,wkzpkr wkzp^setkX%>
wae` eov{p"eop,eop hmp^setkX^setkX%>
wae` a{pv{p"eop o{hjkz,eop hmp^setkX^setkX%>
] $eoskzpQ}{k{k"eop wkzpkrQoa,]$gezsp%>
] $`klkpkQ}{k{k"eop $wkzpkrQoa,]$gezsp%>
x>
!!eoskzp wkzpkr eopa caookcpewepu lesp
K`ik$jzkm`pbQgezspQskmzcb44eoskzpQwkzpkr"eop wkzpkrQoa,k`ik$gezsp%
~
K`ik$okyl,$c{zzkop>
okyl8oky"k`ik%>
okyl(?pkzheoml8wkzpkrQoa>
okyl(?okrp8o{ll>
eg"-gezsp%
zkp{zo"okyl%>
gaz"c{zzkop8gezsp>c{zzkop(?okrp>c{zzkop8c{zzkop(?okrp%>
c{zzkop(?okrp8okyl>
zkp{zo"gezsp%>
x
!!eoskzp wml{ks eopa }{k{ks
]$jzkm`pbQgezspQskmzcb44eoskzpQ}{k{k"eop wkzpkrQoa,]$gezsp%
~
]$oky,$c{zzkop>
okyl8oky"]%>
okyl(?eoga8wkzpkrQoa>
okyl(?okrp8o{ll>
eg"-gezsp%
zkp{zo"okyl%>
8/3/2019 Data Algorithm And Design
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8/3/2019 Data Algorithm And Design
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Eg"hmpzer^eX^dX?6%
Wkzp^eX/k`ikQvpz8eoskzpQwkzpkr"d,wkzp^eX/k`ikQvpz%>
x
!!cahv{peoi vmpb lkoipb
wae` jzk`pbQgezspQskmzcb44JGS"eop eo`kr,wkzpkr wkzp^setkX%
~
] $}{k{k8o{ll>
k`ik$leon>
wkzp^eo`krX/wesep8p>
}{k{k8eoskzpQ}{k{k"eo`kr,}{k{k%>
ybelk"}{k{k%
~
}{k{k8`klkpkQ}{k{k"'eo`kr,}{k{k%>
gaz"leon8wkzp^eo`krX/k`ikQvpz>leon>leon8leon(?okrp%
~
eg"wkzp^leon(?pkzheomlx/wesep88g%
~
wkzp^leon(?pkzheomlx/wesep8p>
wkzp^leon?pkzheomlX/vmpbQlkoibp8wkzp^eo`krX/vmpbQlkoibp.=>
}{k{k8eoskzpQ}{k{k"leon(?pkzheoml,}{k{k%>
x
x
x
x
!!eov{p g{ocpeao pa zkm` m`dmckocu hmpzer
wae` jzkm`pbQgezspQskmzcb44eov{p"eop o{hjkz,eop hmp^setkX^setkX%
8/3/2019 Data Algorithm And Design
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~
ca{pdd..%
~
ceo??hmp^eX^dX>
x
ca{pee..%
~
gaz"eop d86>dd..%
~
ca{p
jzkm`pbQgezspQskmzcb JQGQS>
http://output/http://output/http://function/http://function/http://function/http://output/8/3/2019 Data Algorithm And Design
21/46
eop o{hjkz,eo`kr>
eop hmp^setkX^setkX>
wkzpkr wkzp^setkX>
K`ik$lesp>
ca{p
JQGQS/eov{p"o{hjkz,hmp%>
JQGQS/a{pv{p"o{hjkz,hmp%>
JQGQS/pmjlk"o{hjkz,hmp,wkzp%>
ca{pee..%
~
ca{p
x
x
ikpcb"%>
x
8/3/2019 Data Algorithm And Design
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A[PV[P4
eov{p pbk oa/ ag wkzpecks eo pbk izmvb42
eov{p pbk m`dmckocu hmpzer6 = 6 6 6 = 6 6
6 = 6 6 6 6 = 6
6 6 6 6 = 6 = =
6 6 6 = 6 6 6 =
= = 6 6 6 6 6 6
6 6 = = 6 6 6 =
6 6 6 = = 6 = 6
= 6 6 6 = 6 6 =
m`dmckocu hmpzer
6 = 6 6 6 = 6 66 = 6 6 6 6 = 6
6 6 6 6 = 6 = =
6 6 6 = 6 6 6 =
= = 6 6 6 6 6 6
6 6 = = 6 6 6 =
6 6 6 = = 6 = 6
= 6 6 6 = 6 6 =
eov{p pbk spmzpeoi wkzpkr 6(9
vmpb lkoipb ag pbk wkzpkr gzah M
wkzpkr lkoipb wkzpkr caookcpewepu
M 6 J G
J = J I
C : K I B
@ : @ BK 3 M J
G = C @ B
I : @ K I
B : M K B
8/3/2019 Data Algorithm And Design
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Vzaizmh Oa(7
MEH4 Pa yzepk mo mliazepbh mo` m vzaizmh pa ehvlkhkop `kvpb gezsp skmzcb/
MLIAZEPBH
@GS I"w, k%
=/ lesp L 8 khvpu
:/ pzkk P 8 khvpu
3/ cbaask m spmzpeoi wkzpkr r0/ skmzcb"r%
;/ ybelk"L es oap khvpu%
7/ zkhawk k`ik "w, y% gzah jkieooeoi ag L
9/ egy oap ukp wesepk`
2/ m`` "w, y% pa P
5/ skmzcb"y%
=6/skmzcb"wkzpkr w%
==/ wesep w
=:/gaz kmcb k`ik "w, y%
=3/ m`` k`ik "w, y% pa pbk jkieooeoi ag L
VZAIZMH PA EHVKHKOP @KVPB GEZSP SKMZCB
#eocl{`k
8/3/2019 Data Algorithm And Design
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eop m^=6X^=6X>
eop o,e,d,s^=6X,g^=6X,calaz^=6X,pehk,{>
wae` `QgQs"eop {%
~
calaz^{X8izmu>
pehk8pehk.=>
s^{X8pehk>
gaz"d8=>dd..%
~
eg""m^{X^dX-86%''"calaz^dX88ybepk%%
`QgQs"d%>
x
calaz^{X8jlmcn>
pehk8pehk.=>
g^{X8pehk>
x
wae` vmzkopbkses"%
~
gaz"e8=>ee..%
~
gaz"d8=>dd..%
~
eg"e88s^dX%
vzeopg"*"+`*,d%>
eg"e88g^dX%
vzeopg"*+`%*,d%>
x
x
x
wae` hmeo"%
~
8/3/2019 Data Algorithm And Design
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clzscz"%>
vzeopg"*kopkz pbk oa/ ag wkzpecks 4*%>
scmog"*+`*,'o%>
vzeopg"*\oKOPKZ PBK M@DMCKOCU HMPZER AG IZMVB \o*%>
gaz"e8=>ee..%
~
gaz"d8=>dd..%
~
scmog"*+`*,'m^eX^dX%>
x
vzeopg"*\o*%>
x
vzeopg"*\o PBK M@DMCKOCU HMPZER AG IZMVB \o*%>
gaz"e8=>ee..%
~
calaz^eX8ybepk>
g^eX86>
s^eX86>
gaz"d8=>dd..%
~
vzeopg"*+` *,m^eX^dX%>
x
vzeopg"*\o*%>
x
pehk86>
gaz"e8=>ee..%
~
eg"calaz^eX88ybepk%
`QgQs"e%>
x
vzeopg"*\OMGPKZ MVVLUEOI @(G(S MLIAZEPBH\o*%>
8/3/2019 Data Algorithm And Design
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vzeopg"*WKZPKR SPEHK GPEHK\o*%>
gaz"e8=>ee..%
~
vzeopg"*+` +` +`\o*,e,s^eX,g^eX%>
x
vzeopg"*\o\o VMZKOPBKSES SPZ[CP[ZK ES MS GALLAYS 4\o*%>
vmzkopbkses"%>
ikpcb"%>
x
A[PV[P4
kopkz pbk oa/ ag wkzpecks 40
KOPKZ PBK M@DMCKOCU HMPZER AG IZMVB
6
=
=
6
=
6
6
=
=
6
6
6
6
=
8/3/2019 Data Algorithm And Design
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6
6
kopkz pbk sa{zck wkzpkr 4:
PBK M@DMCKOCU HMPZER AG IZMVB
6 = = 6
= 6 6 =
= 6 6 6
6 = 6 6
MGPKZ MVVLUEOI JGS MLIAZEPBH A[PV[P ES 4
VMPB PA JK GALLAYK@ PA ZKMCB PBK WKZPKR = es 4((:((=
LKOIPB8=
VMPB PA JK GALLAYK@ PA ZKMCB PBK WKZPKR : es 4((:
LKOIPB86
VMPB PA JK GALLAYK@ PA ZKMCB PBK WKZPKR 3 es 4((:((=((3
LKOIPB8:
VMPB PA JK GALLAYK@ PA ZKMCB PBK WKZPKR 0 es 4((:((0
LKOIPB8=
8/3/2019 Data Algorithm And Design
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Vzaizmh Oa(9
MEH4 Payzepk mo mliazepbh mo` m vzaizmh pa ehvlkhkop Ca{opeoi Sazp/
MLIAZEPBH
=/ gaz e 6 pa n:/ `a C^eX 63/ gaz d = pa lkoipb^MX0/ `a C^M^dXX C^M^dXX.=;/
gaz e = pa n
7/ `a C^eX C^eX.C^e(=X9/ gaz d lkoipb^MX `ayo pa =2/ `a J^C^M^dXXX M^dX5/ C^M^dXX C^M^dXX(=
VZAIZMH PA EHVLKHKOP CA[OPEOI SAZP
#eocl{`k
vzeopg"bay hmou o{hjkzs `a { ymop pa sazp\o\o%>
scmog"+`,'o%>
vzeopg"\o kopkz pbk o{hjkzs\o\o%>
gaz"e8=>ee..%
8/3/2019 Data Algorithm And Design
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scmog"+`,'m^eX%>
n8m^=X>
gaz"e8:>ee..%
eg"n8m^=X%
n8m^eX>
gaz"e86>ed..%
c^eX86>
gaz"d8=>dd..%
c^m^dX8c^m^dXX.=>
gaz"d8o>d?8=>d((%
~
j^c^m^dXX8m^dX>
c^m^dXX8c^m^dXX(=>
x
vzeopg"\o pbk sazpk` lesp ju ca{opeoi sazps es \o%>
gaz"e8=>ee..%
vzeopg"\o+`,j^eX%>
ikpcb"%>
x
A[PV[P4
bay hmou o{hjkzs `a { ymop pa sazp
;
kopkzs pbk o{hjkzs
=6
=:
;7
57
2;
8/3/2019 Data Algorithm And Design
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pbk sazpk` lesp ju ca{opeoi sazps es
=6
=:
;7
2;
57
8/3/2019 Data Algorithm And Design
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Vzaizmh Oa(2
MEH4 Pa yzepk mo mliazepbh mo` m vzaizmh pa ehvlkhkop hmpzer cbmeo
h{lpevlecmpeao
MLIAZEPBH
HMPZER H[LPEVLU"M, J%
=/ eg cal{hos^MX -8 zays^JX:/ pbko kzzazeocahvmpejlk `ehkoseaos3/
klsk gaz e = pa zays^MX
0/ `a gaz d = pa cal{hos^JX;/ `a c^e,dX 67/ gaz n = pa cal{hos^MX9/ `a C^e,dX C^e,dX.M^e,nX/J^n,dX2/ zkp{zo C
VZAIZMH PA EHVLKHKOP HMPZER CBMEO H[LPEVLECMPEAO
#eocl{`k
eop e,d,n,o87,v^9X,l>
clzscz"%>
8/3/2019 Data Algorithm And Design
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vzeopg"kopkz pbk wml{k gaz pbk `ehkoseaos\o%>
gaz"e86>ee..%
~
scmog"+`,'v^eX%>
x
gaz"e8=>ee..%
~
h^eX^dX86>
x
gaz"l8:>ll..%
~
gaz"e8=>en
Eg"}
s^eX^dX8n>
x
x
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clzscz"%>
vzeopg"pbk heoeh{h ha/ Ag scmlmz h{lpevlecmpeao h^eX^dX es\o\o%>
gaz"e8=>ee..%
~
gaz"d8e>dd..%
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~
vzeopg"+ \p,h^eX^dX%>
vzeopg"\o%>
x
x
vzeopg"\o m{rellmzu pmjlk zkcaz`s pbk eo`kr ag n mcbekwk`%>
vzeopg"avpehml casp eo cahv{peoi h^eX^dX\o\o%>
gaz"e8=>ee..%
~
gaz"d8=>dd..%
~
vzeopg"+ \p,s^eX^dX%>
vzeopg"\o%>
x
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vzeopg"\o pbk avpehml sal{peao es\o\o%>
vzeop avpehml vmzkos "=,o%>
ikpcb"%>
x
wae` vzeop avpehml vmzkos "eop e,eop d%
~
eg"e8d%
vzeopg"M+`,e%>
klsk
~
vzeopg"" %>
vzeop avpehml vmzkos "e,s^eX^dX%>
vzeop avpehml vmzkos "s^eX^dX.=,d%>
vzeopg"% %>
x
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A[PV[P4
kopkz pbk wml{ks gaz `ehkoseaos
:63
7
=;
:6
=6
=:
pbk heoeh{h oa/ ag scmlmz h{lpevlecmpeao h^eX^dX es
6 376 ==96 :396 :396 :2;6
6 :96 ==96 =996 :=36
6 =266 3666 39:6
6 3666 0266
6 :066
6
m{rellmzu pmjlk zkcaz`s pbk eo`kr ag n mcbekwk` pbk avpehml casp eo cahv{peoi h^eX^dX
6 = = = = =
6 : 3 0 ;
6 3 0 ;
6 0 ;
6 ;
pbk avpehml sal{peao es
"M=""""M: M3%M0%M;%M7%%
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Vzaizmh Oa(5
MEH4 Pa yzepk mo mliazepbh mo` m vzaizmh pa ehvlkhkop mcpewepu sklkcpeao
vzajlkh/
MLIAZEPBH
Mcpewepu sklkcpaz"s,g%
=/ olkoipb^sX
:/ M ~m=x
3/ e =
0/ gaz h : pa o
;/ `a eg sh?8ge
7/ pbko M M [ ~mhx
9/ e h
2/ zkp{zo M
VZAIZMH PA EHVLKHKOP MCPEWEPU SKLKCPEAO VZAJLKH
# eocl{`k
vzeopg"bay hmou mcpewepks\o%>
scmog"+`,'o%>
vzeopg"\o kopkz pbk spmzpeoi pehk gaz mcpewepks\o%>
gaz"e8=>ee..%
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scmog"+`,'s^eX%>
vzeopg"\o kopkz pbk geoesbeoi pehk gaz pbk mcpewepks\o%>
gaz"e8=>ee..%>
scmog"+`,'g^eX%>
vzeopg"\o pbk mcpewepu az`kz es \o\o%>
vzeopg"M=%>
e8=>
gaz"h8:>hh..%
eg"s^hX?8g^eX%
~
vzeopg"\pM+`,h%>
e8h>
x
ikpcb"%>
x
A[PV[P4
bay hmou mcpewepks
:
kopkz pbk spmzpeoi pehk gaz mcpewepks
:
3
kopkz pbk geoesbeoi pehk gaz pbk mcpewepks
0
pbk mcpewepu az`kz es
M= M:
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Vzaizmh Oa(=6
MEH4 Pa yzepk mo mliazepbh mo` m vzaizmh pa ehvlkhkop laoiksp cahhao
s{jsk}{kock/
MLIAZEPBH
=/ LCS(LKOIPB"R,U%:/ hlkoipb^RX3/ olkoipb^UX0/ gaze= pa h
e/
`ac^e,6X6;/ gazd6 pa o
e/ `ac^6,dX67/ gaze= pa h
e/ `a gazd= pa o=/ `a egre 8ud
m/ pbkoc^e,dXc^e(=,d(=X.=e/ j^e,dX
j/ klsk egc^e(=,dXc^e,d(=Xe/ pbkoc^e,dXc^e(=,dX
=/ j^e,dXee/ klskc^e,dXc^e,d(=X
=/ j^e,dX9/ zkp{zo c mo` j
VZEOP(LCS"j,R,e,d%
=/ Ege86 az d86e/ pbko zkp{zo
:/ egj^e,dX8 e/ pbko VZEOP(LCS"j,R,e(=,d(=%
ee/ vzeop re
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3/ klskegj^e,dX8e/ pbko VZEOP(LCS"j,R,e(=,d%
0/ klsk VZEOP(LCS"j,R,e,d(=%
VZAIZMH PA EHVLKHKOP LAOIKSP CAHHAO S[JSK][KOCK
#eocl{`k
clzscz"%>
vzeopg"*Kopkz pbk lkoipb ag gezsp sk}{kock48*%>
ggl{sb"sp`eo%>
scmog"*+`*,'h%>
vzeopg"*Kopkz pbk gezsp sk}{kock48*%>
gaz"e8=>ee..%
~ ggl{sb"sp`eo%>
scmog"*+c*,'r^eX%>
x
vzeopg"*Kopkz pbk lkoipb ag skcao` sk}{kock48*%>
ggl{sb"sp`eo%>
scmog"*+`*,'o%>
vzeopg"*Kopkz pbk skcao` sk}{kock48*%>
gaz"e8=>ee..%
~
ggl{sb"sp`eo%>
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scmog"*+c*,'u^eX%>
x
gaz"e8=>ee..%
~
c^eX^6X86>
x
gaz"d86>dd..%
~
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~
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~
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~
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j^eX^dX8=6>
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klsk
eg"c^e(=X^dX?8c^eX^d(=X%
~
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klsk
~
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x
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x
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vzeopg"*Pbk laoiksp cahhao s{jsk}{kock es4*%>
vzeop"h,o%>
ikpcb"%>
x
wae` vzeop"eop e,eop d%
~
eg"e886||d886%
~
zkp{zo>
x
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~
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eg"j^eX^dX88:6%
~
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x
klsk
vzeop"e,d(=%>
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A[PV[P4
Kopkz pbk lkoipb ag gezsp sk}{kock483
Kopkz pbk gezsp sk}{kock48M
J
C
Kopkz pbk lkoipb ag skcao` sk}{kock48;
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Kopkz pbk skcao` sk}{kock48M
S
@
J
@
Pbk laoiksp cahhao s{jsk}{kock es4MJ
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Vzaizmh Oa(==
MEH4 Pa yzepk mo mliazepbh mo` m vzaizmh pa ehvlkhkop @ednspzms mlia gaz
seoilk sa{zck sbazpksp vmpb/
MLIAZEPBH
= g{ocpeao @ednspzm"Izmvb, sa{zck%4
: gaz kmcb wkzpkr w eo Izmvb4 !! Eoepemletmpeaos
3 `esp^wX 48 eogeoepu !! [onoayo `espmock g{ocpeao gzah s pa w
0 vzkwea{s^wX 48 {o`kgeok`
; `esp^sa{zckX 48 6 !! @espmock gzah s pa s
7 ] 48 cavu"Izmvb% !! Skp ag mll {owesepk` wkzpecks
9 ybelk]es oap khvpu4 !! Pbk hmeo laav
2 { 48 krpzmcpQheo"]% !! Zkhawk jksp wkzpkr gzah vzeazepu }{k{k> zkp{zos
sa{zck ao gezsp epkzmpeao
5 gaz kmcb okeibjaz w ag{4
=6 mlp8 `esp^{X . lkoipb"{, w%
== egmlp< `esp^wX !! Zklmr "{,w%
=: `esp^wX 48 mlp
=3 vzkwea{s^wX 48 {
VZAIZMH PA EHVLKHKOP @EDNSPZMS MLIA GAZ SEOILK SA[ZCK
SBAZPKSP VMPB
#eocl{`k
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~
eg"n88s%
vzeopg"*((+`*,s%>
klsk
eg"vzk^nX886%
vzeopg"*oa vmpb gzah sa{zck pa wkzpkr*%>
klsk
~
vzeopvmpb"vzk^nX%>
vzeopg"*((+`*,n%>
x
x
wae` hmeo"%
~
clzscz"%>
vzeopg"*kopkz pbk oa/ ag wkzpecks 4*%>
scmog"*+`*,'o%>
vzeopg"*\oKOPKZ PBK M@DMCKOCU HMPZER AG IZMVB \o*%>
gaz"e8=>ee..%
~
gaz"d8=>dd..%
~
scmog"*+`*,'m^eX^dX%>
x
vzeopg"*\o*%>
x
vzeopg"*kopkz pbk sa{zck wkzpkr 4*%>
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vzeopg"*\o PBK M@DMCKOCU HMPZER AG IZMVB \o*%>
gaz"e8=>ee..%
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~
`^eX8555>
c^eX86>
vzk^eX86>
gaz"d8=>dd..%
~
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x
vzeopg"*\o*%>
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~
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vzk^eX8pkhv>
pkhv=8e>
x
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pkhv8pkhv=>
gaz"e8=>ee..%
~
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x
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vzeopg"*\oMGPKZ MVVLUEOI @EDNSPZM MLIAZEPBH A[PV[P ES 4\o*%>
gaz"e8=>ee..%
~
eg"e-8s%
~
vzeopg"*\osbazpksp `espmock gzah sa{zck pa +` 4+` mo` vmpb gallayk` es *,e,`^eX%>
vzeopvmpb"e%>
x
x
ikpcb"%>
x
A[PV[P4
kopkz pbk oa/ ag wkzpecks 43
KOPKZ PBK M@DMCKOCU HMPZER AG IZMVB
6
=6
;
6
6
:
6
3
6
kopkz pbk sa{zck wkzpkr 4=
PBK M@DMCKOCU HMPZER AG IZMVB
8/3/2019 Data Algorithm And Design
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6 =6 ;
6 6 :
6 3 6
MGPKZ MVVLUEOI @EDNSPZM MLIAZEPBH A[PV[P ES 4
sbazpksp `espmock gzah sa{zck pa : 42 mo` vmpb gallayk` es ((=((3((:
sbazpksp `espmock gzah sa{zck pa 3 4; mo` vmpb gallayk` es ((=((3